No, solubility is when a compound is fully dissolved. If there is any separation from the solution, it isn't dissolved. This is the case if the separation are solid particles (sol colloids), liquid particles (emulsion), etc. Look up colloids. If a compound forms micelles it is still separated from solution, even if the solution looks clear. So to find the true solubility, you need to separate the micelles from the saturated monomer solution. As to your question, I don't know the proper use of Aq, because since graduating from my chemistry degree 8 years ago, I've never written out a chemical equation. But I'm assuming that Aq should mean a fully dissolved solute. Precipitation should be (s), but ALL compounds have solubility, so you will always have some still dissolved at the solubility of the solute at the given solvent composition and temperature. Normally you try to cool to crash more product out so you can increase yield. This happens because you reduce solubility by cooling, so less can dissolve. It may be the difference between a 70% yield and 90% yield.